"""
Copyright, the CVXPY authors

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""

import logging
from typing import Any, Dict, Generic, Iterator, List, Optional, Tuple, Union

import numpy as np
from scipy.sparse import dok_matrix

import cvxpy.settings as s
from cvxpy import Zero
from cvxpy.constraints import SOC, ExpCone, NonNeg
from cvxpy.reductions.dcp2cone.cone_matrix_stuffing import ParamConeProg
from cvxpy.reductions.solution import Solution, failure_solution
from cvxpy.reductions.solvers import utilities
from cvxpy.reductions.solvers.conic_solvers.conic_solver import (
    ConicSolver,
    dims_to_solver_dict,
)

log = logging.getLogger(__name__)

try:
    # Try to import SCIP model for typing
    from pyscipopt.scip import Model as ScipModel
except ModuleNotFoundError:
    # If it fails continue and use a generic type instead.
    ScipModel = Generic


# Mapping of SCIP to cvxpy status codes
STATUS_MAP = {
    # SOLUTION_PRESENT
    "optimal": s.OPTIMAL,
    "timelimit": s.OPTIMAL_INACCURATE,
    "gaplimit": s.OPTIMAL_INACCURATE,
    "nodelimit": s.OPTIMAL_INACCURATE,
    "totalnodelimit": s.OPTIMAL_INACCURATE,
    "bestsollimit": s.USER_LIMIT,
    # INF_OR_UNB
    "infeasible": s.INFEASIBLE,
    "unbounded": s.UNBOUNDED,
    "inforunbd": s.INFEASIBLE_OR_UNBOUNDED,
    # ERROR
    "userinterrupt": s.SOLVER_ERROR,
    "memlimit": s.SOLVER_ERROR,
    "sollimit": s.SOLVER_ERROR,
    "stallnodelimit": s.SOLVER_ERROR,
    "restartlimit": s.SOLVER_ERROR,
    "unknown": s.SOLVER_ERROR,
}


class ConstraintTypes:
    """Constraint type constants."""
    EQUAL = "EQUAL"
    LESS_THAN_OR_EQUAL = "LESS_THAN_OR_EQUAL"


class VariableTypes:
    """Variable type constants."""
    BINARY = "BINARY"
    INTEGER = "INTEGER"
    CONTINUOUS = "CONTINUOUS"


class SCIP(ConicSolver):
    """An interface to the SCIP solver."""

    MIP_CAPABLE = True
    SUPPORTED_CONSTRAINTS = ConicSolver.SUPPORTED_CONSTRAINTS + [SOC]
    MI_SUPPORTED_CONSTRAINTS = SUPPORTED_CONSTRAINTS

    def name(self) -> str:
        """The name of the solver."""
        return 'SCIP'

    def import_solver(self) -> None:
        """Imports the solver."""
        import pyscipopt
        pyscipopt

    def apply(self, problem: ParamConeProg) -> Tuple[Dict, Dict]:
        """Returns a new problem and data for inverting the new solution."""

        # Create data and inv_data objects
        data = {}
        inv_data = {self.VAR_ID: problem.x.id}
        if not problem.formatted:
            problem = self.format_constraints(problem, None)
        data[s.PARAM_PROB] = problem
        data[self.DIMS] = problem.cone_dims
        inv_data[self.DIMS] = problem.cone_dims

        constr_map = problem.constr_map
        inv_data[self.EQ_CONSTR] = constr_map[Zero]
        inv_data[self.NEQ_CONSTR] = (
            constr_map[NonNeg]
            + constr_map[SOC]
            + constr_map[s.PSD]
            + constr_map[ExpCone]
        )

        # Apply parameter values.
        # Obtain A, b such that Ax + s = b, s \in cones.
        c, d, A, b = problem.apply_parameters()
        data[s.C] = c
        inv_data[s.OFFSET] = d
        data[s.A] = -A
        data[s.B] = b
        # return data, inv_data

        # data, inv_data = super(SCIP, self).apply(problem)
        variables = problem.x

        # Use of sets here is minor lift to speed up get_variable_type(...) below.
        data[s.BOOL_IDX] = set(int(t[0]) for t in variables.boolean_idx)
        data[s.INT_IDX] = set(int(t[0]) for t in variables.integer_idx)
        inv_data['is_mip'] = data[s.BOOL_IDX] or data[s.INT_IDX]

        return data, inv_data

    def invert(self, solution: Dict[str, Any], inverse_data: Dict[str, Any]) -> Solution:
        """Returns the solution to the original problem given the inverse_data."""

        status = solution['status']
        dual_vars = None

        if status in s.SOLUTION_PRESENT:
            opt_val = solution['value'] + inverse_data[s.OFFSET]
            primal_vars = {inverse_data[SCIP.VAR_ID]: solution['primal']}

            if "eq_dual" in solution and not inverse_data['is_mip']:
                eq_dual = utilities.get_dual_values(
                    result_vec=solution['eq_dual'],
                    parse_func=utilities.extract_dual_value,
                    constraints=inverse_data[SCIP.EQ_CONSTR],
                )
                leq_dual = utilities.get_dual_values(
                    result_vec=solution['ineq_dual'],
                    parse_func=utilities.extract_dual_value,
                    constraints=inverse_data[SCIP.NEQ_CONSTR],
                )

                eq_dual.update(leq_dual)
                dual_vars = eq_dual

            return Solution(status, opt_val, primal_vars, dual_vars, {})
        else:
            return failure_solution(status)

    def solve_via_data(
            self,
            data: Dict[str, Any],
            warm_start: bool,
            verbose: bool,
            solver_opts: Dict[str, Any],
            solver_cache: Dict = None,
    ) -> Solution:
        """Returns the result of the call to the solver."""
        from pyscipopt.scip import Model

        model = Model()
        model.redirectOutput()
        A, b, c, dims = self._define_data(data)
        variables = self._create_variables(model, data, c)
        constraints = self._add_constraints(model, variables, A, b, dims)
        self._set_params(model, verbose, solver_opts, data, dims)
        solution = self._solve(model, variables, constraints, data, dims)

        return solution

    def _define_data(self, data: Dict[str, Any]) -> Tuple:
        """Define data parts from the data reference."""
        c = data[s.C]
        b = data[s.B]
        A = dok_matrix(data[s.A])
        # Save the dok_matrix.
        data[s.A] = A
        dims = dims_to_solver_dict(data[s.DIMS])
        return A, b, c, dims

    def _create_variables(self, model: ScipModel, data: Dict[str, Any], c: np.ndarray) -> List:
        """Create a list of variables."""
        variables = []
        for n, obj in enumerate(c):
            var_type = get_variable_type(n=n, data=data)
            variables.append(
                model.addVar(
                    obj=obj,
                    name="x_%d" % n,
                    vtype=var_type,
                    lb=None if var_type != VariableTypes.BINARY else 0,
                    ub=None if var_type != VariableTypes.BINARY else 1,
                )
            )
        return variables

    def _add_constraints(
            self,
            model: ScipModel,
            variables: List,
            A: dok_matrix,
            b: np.ndarray,
            dims: Dict[str, Union[int, List]],
    ) -> List:
        """Create a list of constraints."""

        # Equal constraints
        equal_constraints = self.add_model_lin_constr(
            model=model,
            variables=variables,
            rows=range(dims[s.EQ_DIM]),
            ctype=ConstraintTypes.EQUAL,
            A=A,
            b=b,
        )

        # Less than or equal constraints
        leq_start = dims[s.EQ_DIM]
        leq_end = dims[s.EQ_DIM] + dims[s.LEQ_DIM]
        inequal_constraints = self.add_model_lin_constr(
            model=model,
            variables=variables,
            rows=range(leq_start, leq_end),
            ctype=ConstraintTypes.LESS_THAN_OR_EQUAL,
            A=A,
            b=b,
        )

        # Second Order Cone constraints
        soc_start = leq_end
        soc_constrs = []
        new_leq_constrs = []
        for constr_len in dims[s.SOC_DIM]:
            soc_end = soc_start + constr_len
            soc_constr, new_leq, new_vars = self.add_model_soc_constr(
                model=model,
                variables=variables,
                rows=range(soc_start, soc_end),
                A=A,
                b=b,
            )
            soc_constrs.append(soc_constr)
            new_leq_constrs += new_leq
            variables += new_vars
            soc_start += constr_len

        return equal_constraints + inequal_constraints + new_leq_constrs + soc_constrs

    def _set_params(
            self,
            model: ScipModel,
            verbose: bool,
            solver_opts: Optional[Dict],
            data: Dict[str, Any],
            dims: Dict[str, Union[int, List]],
    ) -> None:
        """Set model solve parameters."""
        from pyscipopt import SCIP_PARAMSETTING

        # Set model verbosity
        hide_output = not verbose
        model.hideOutput(hide_output)

        # General kwarg params
        scip_params = solver_opts.pop("scip_params", {})
        if solver_opts:
            try:
                model.setParams(solver_opts)
            except KeyError as e:
                raise KeyError(
                    "One or more solver params in {} are not valid: {}".format(
                        list(solver_opts.keys()),
                        e,
                    )
                )

        # Scip specific params
        if scip_params:
            try:
                model.setParams(scip_params)
            except KeyError as e:
                raise KeyError(
                    "One or more scip params in {} are not valid: {}".format(
                        list(scip_params.keys()),
                        e,
                    )
                )

        is_mip = data[s.BOOL_IDX] or data[s.INT_IDX]
        has_soc_constr = len(dims[s.SOC_DIM]) > 1
        if not (is_mip or has_soc_constr):
            # These settings are needed  to allow the dual to be calculated
            model.setPresolve(SCIP_PARAMSETTING.OFF)
            model.setHeuristics(SCIP_PARAMSETTING.OFF)
            model.disablePropagation()

    def _solve(
            self,
            model: ScipModel,
            variables: List,
            constraints: List,
            data: Dict[str, Any],
            dims: Dict[str, Union[int, List]],
    ) -> Dict[str, Any]:
        """Solve and return a solution if one exists."""

        try:
            model.optimize()
        except Exception as e:
            log.warning("Error encountered when optimising %s: %s", model, e)

        solution = {}

        if max(model.getNSols(), model.getNCountedSols()) > 0:
            sol = model.getBestSol()
            solution["primal"] = np.array([sol[v] for v in variables])

            # HACK can't get objective value directly if stopped due to time limit.
            if model.getStatus() == 'timelimit':
                # the solution value is not actually necessary
                # since CVXPY calculates it by evaluating the objective
                # at the solution.
                solution["value"] = np.nan
            else:
                solution["value"] = model.getObjVal()

            is_mip = data[s.BOOL_IDX] or data[s.INT_IDX]
            has_soc_constr = len(dims[s.SOC_DIM]) > 1
            if not (is_mip or has_soc_constr):
                # Not the following code calculating the dual values does not
                # always return the correct values, see tests `test_scip_lp_2`
                # and `test_scip_socp_1`.
                vals = []

                # Get linear duals.
                for lc in constraints:
                    if lc is not None and lc.isLinear():
                        dual = model.getDualsolLinear(lc)
                        vals.append(dual)

                solution["y"] = -np.array(vals)
                solution[s.EQ_DUAL] = solution["y"][0:dims[s.EQ_DIM]]
                solution[s.INEQ_DUAL] = solution["y"][dims[s.EQ_DIM]:]

        solution[s.SOLVE_TIME] = model.getSolvingTime()
        solution["status"] = STATUS_MAP[model.getStatus()]
        if solution["status"] == s.SOLVER_ERROR and model.getNCountedSols() > 0:
            solution["status"] = s.OPTIMAL_INACCURATE

        if model.getStatus() == 'timelimit' \
                and model.getNCountedSols() == 0 \
                and model.getNSols() == 0:
            solution["status"] = s.SOLVER_ERROR

        if model.getStatus() == 'timelimit' \
                and (model.getNSols() > 0 \
                or model.getNCountedSols() > 0):
            solution["status"] = s.OPTIMAL_INACCURATE

        return solution

    def add_model_lin_constr(
        self,
        model: ScipModel,
        variables: List,
        rows: Iterator,
        ctype: str,
        A: dok_matrix,
        b: np.ndarray,
    ) -> List:
        """Adds EQ/LEQ constraints to the model using the data from mat and vec.

        Return list contains constraints.
        """
        from pyscipopt.scip import quicksum

        constraints = []
        expr_list = {i: [] for i in rows}
        for (i, j), c in A.items():
            v = variables[j]
            try:
                expr_list[i].append((c, v))
            except Exception:
                pass

        for i in rows:
            # Ignore empty constraints.
            if expr_list[i]:
                expression = quicksum(coeff * var for coeff, var in expr_list[i])
                constraint = model.addCons(
                    (expression == b[i])
                    if ctype == ConstraintTypes.EQUAL
                    else (expression <= b[i])
                )
                constraints.append(constraint)
            else:
                constraints.append(None)

        return constraints

    def add_model_soc_constr(
        self,
        model: ScipModel,
        variables: List,
        rows: Iterator,
        A: dok_matrix,
        b: np.ndarray,
    ) -> Tuple:
        """Adds SOC constraint to the model using the data from mat and vec.

        Return tuple contains (QConstr, list of Constr, and list of variables).
        """
        from pyscipopt.scip import quicksum

        # Assume first expression (i.e. t) is nonzero.
        expr_list = {i: [] for i in rows}
        for (i, j), c in A.items():
            v = variables[j]
            try:
                expr_list[i].append((c, v))
            except Exception:
                pass

        # Make a variable and equality constraint for each term.
        soc_vars = []
        for i in rows:
            lb = 0 if len(soc_vars) == 0 else None
            var = model.addVar(
                obj=0,
                name="soc_t_%d" % i,
                vtype=VariableTypes.CONTINUOUS,
                lb=lb,
                ub=None,
            )
            soc_vars.append(var)

        lin_expr_list = [
            b[i] - quicksum(coeff * var for coeff, var in expr_list[i])
            for i in rows
        ]

        new_lin_constrs = [
            model.addCons(soc_vars[i] == lin_expr_list[i])
            for i, _ in enumerate(lin_expr_list)
        ]

        # Interesting because only <=?
        t_term = soc_vars[0] * soc_vars[0]
        x_term = quicksum([var * var for var in soc_vars[1:]])
        constraint = model.addCons(x_term <= t_term)

        return (
            constraint,
            new_lin_constrs,
            soc_vars,
        )


def get_variable_type(n: int, data: Dict[str, Any]) -> str:
    """Given an index n, and a set of data,
    return the type of a variable with the same index."""
    if n in data[s.BOOL_IDX]:
        return VariableTypes.BINARY
    elif n in data[s.INT_IDX]:
        return VariableTypes.INTEGER
    return VariableTypes.CONTINUOUS
